As for Roy Hodgson's men, Palace fell to a last-gasp defeat against Manchester United on Monday and still find themselves in the midst of an increasingly tense battle to avoid the drop.
Chelsea head into the crucial stages of the season requiring some of last-term's consistency should they realistically want to earn Champions League football next season.
Sunday's poor display against Manchester City has furthered some of the political plots developing between Conte and the Chelsea hierarchy throughout the season, and it still remains to be seen as to whether the Italian coach will be at the club come the end of the current campaign.
The Blues have now lost four of their last five Premier League outings, following defeats to Bournemouth, Watford, Manchester United and City. Chelsea's last four defeats in the league prior to that were spread across 30 fixtures.
The gap to fourth-placed Tottenham Hotspur currently stands at five points, with the two sides still to play each other on April 1. Before then, though, the Blues also face a key Champions League test against Barcelona as they aim to battle past the Catalans to reach the quarter-finals of the competition.
The landscape for Chelsea might make grim reading for some fans, but those two fixtures still present viable opportunities for Conte and his men to mount a late revival, although they will need to pick up three points against the likes of Crystal Palace and Burnley in the coming weeks should they want to keep those ambitions alive.
Amid the gloom and political turmoil, however, Chelsea do find themselves on a favourable run at home, where they have gone undefeated in nine of their last 10 league fixtures.
Fortress Bridge has also been reinforced by the home form of Belgian stopper Thibaut Courtois, who has kept a clean sheet in five of his last six games at home.
Heading into the local derby, the hosts will likely be looking to Willian to make an impact at Stamford Bridge. The Brazilian has played a part in 16 goals from his last 17 starts across all competitions for the club.
Recent form: WLLWLL
Recent form (all competitions): LWWDLL
The Eagles make the short trip across South London coming off the back of a heartbreaking 3-2 loss at the hands of Manchester United on Monday evening.
Hodgson's side had looked full of industry after building a shock 2-0 lead, only to be thwarted by a late United comeback, capped off by a memorable injury-time volley from Nemanja Matic to seal all three points for Jose Mourinho's men.
The former England boss has already worked miracles at Selhurst Park after a shambolic start to the season, but the measure of the task at hand is visible in the fact that despite a number of crucial and inspired wins, Palace still sit in the bottom three.
An almost-laughable list of injuries has caused endless issues for Hodgson, whose side are now on a three-game losing streak in the league. The club have not lost four on the bounce since a problematic run of eight straight defeats last September.
Despite those statistics making difficult reading, Hodgson's men have battled valiantly and it does not appear that his charges' heads have started to drop just yet.
Wilfried Zaha's injury has of course caused problems going forward for Palace, but the January capture of Alexander Sorloth up top could add some important directness going into the final stages of the season. The striker's strength has caused issues for defences already in his first three games for the club. The recent introduction of Aaron Wan-Bissaka in defence has also seen the youth prospect turn in some promising displays.
Beyond the club's personnel, Palace also have a positive record when going into the derby. A victory on Saturday evening could see the Eagles become only the second away side to claim victory from three consecutive top-flight fixtures at Stamford Bridge since Blackburn Rovers.
Palace's upturn in fortunes at the back-end of last year has ultimately given them hope of pulling off what seemed impossible in the autumn, but they still have a long way to go until they are out of trouble. The Eagles will be well aware that three points would potentially lift them out of the bottom three in a relegation battle that sees 13th-placed Swansea City still just three points off the drop.
Recent form: LDDLLL
The Italian coach has a decision to make after the club's display against City, meaning that he could reinstate either Alvaro Morata or Olivier Giroud up top and bring back Eden Hazard behind a striker.
One positive for Hodgson is that Timothy Fosu-Mensah is available to feature after being out of action against his parent club United.
Chelsea possible starting lineup:
Courtois; Azpilicueta, Rudiger, Christensen; Moses, Drinkwater, Fabregas, Alonso; Willian, Hazard, Morata
Crystal Palace possible starting lineup:
Hennessey; Fosu-Mensah, Tomkins, Kelly; Wan-Bissaka, Riedewald, Milivojevic, McArthur, Schlupp; Sorloth, Benteke
Head To Head
The clubs' last six clashes have all come in the Premier League, whereby Palace have won the previous two games, collecting three points both home and away through 2-1 victories.
The latest of those two wins came at Selhurst Park last October to help inspire a Palace revival. At the Bridge, Palace have won two in a row too, once at the end of last season and once during the start of the 2015-2016 campaign.
Over six games, the honours are now equal with both sides picking up three victories each.
We say: Chelsea 2-1 Crystal Palace
Both managers come into the match with a huge amount of work ahead of them, but it is perhaps embattled Palace who have more at stake on Saturday.
The Eagles have failed to win in their last six matches and they are in need of points to keep apace with the rest of their relegation rivals. That said, Hodgson has a problematic injury list and will be facing a Chelsea side with a point to prove after the defeat to City.
Conte could bring in a genuine frontman and that might be problematic for Palace, as both Willian and Hazard are allowed to operate from a little deeper. The visitors will do well to earn themselves a point on the road.